Finite Group Databasebeta

← C13×#11517 #15697856

Subgroups — C13×#11517 #15697856

Order 3328.

750 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 750 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#385C211yesmaximal, characteristic
2C13×#1462C211yesmaximal, characteristic
3C13×#1462C211yesmaximal, characteristic
4C13×#1326C214yesmaximal, complemented
5C24×C4×C13C411yescharacteristic
6C22×C13×C4⋊C4—21no—
7C22×C13×C22⋊C4C411yescharacteristic
8C22×C13×C22⋊C4C2211yescharacteristic
9C13×#407—21no—
10C13×#407—21no—
11C13×#385—21no—
12C13×#385—21no—
13C13×#385C412yes—
14C13×#385C2212yes—
15C2×C13×#95—21no—
16C13×#323—21no—
17C13×#323—21no—
18C13×#323C2212yes—
19C13×#323C2212yes—
20C25×C13C2×C411yescharacteristic
21C23×C4×C13—21no—
22C23×C4×C13—21no—
23C23×C4×C13—21no—
24C23×C4×C13—44no—
25C23×C4×C13—41no—
26C23×C4×C13—41no—
27C23×C4×C13C2×C412yes—
28C23×C4×C13D411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C2×C13×M16—41no—
31C2×C13×M16—41no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4—44no—
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—24no—
37C2×C13×C22⋊C4—41no—
38C2×C13×C22⋊C4—41no—
39C2×C13×C22⋊C4C2×C412yes—
40C2×C13×C22⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4D411yescharacteristic
42C2×C13×C22⋊C4D411yescharacteristic
43C2×C13×C22⋊C4C2311yescharacteristic
44C13×C22⋊C8—22no—
45C13×C22⋊C8—22no—
46C13×C22⋊C8—41no—
47C13×C22⋊C8—41no—
48C13×#95—22no—
49C13×#95—22no—
50#11517C1311yesmaximal, characteristic, direct product factor, Sylow
51C24×C13—21no—
52C24×C13—21no—
53C24×C13—22no—
54C24×C13—22no—
55C24×C13—42no—
56C24×C13—42no—
57C24×C13C22⋊C411yescharacteristic
58C24×C13C22⋊C411yescharacteristic
59C24×C13C22×C411yescharacteristic
60C22×C4×C13—24no—
61C22×C4×C13—24no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—44no—
69C22×C4×C13—44no—
70C22×C4×C13—42no—
71C22×C4×C13—42no—
72C22×C4×C13—42no—
73C22×C4×C13—42no—
74C22×C4×C13—48no—
75C22×C4×C13—44no—
76C22×C4×C13—41no—
77C22×C4×C13—41no—
78C22×C4×C13—42no—
79C22×C4×C13—44no—
80C22×C4×C13—42no—
81C22×C4×C13—42no—
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C22⋊C411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C13×M16—82no—
87C13×M16—82no—
88C2×C8×C13—42no—
89C2×C8×C13—42no—
90C13×C4⋊C4—44no—
91C13×C4⋊C4—44no—
92C13×C22⋊C4—24no—
93C13×C22⋊C4—22no—
94C13×C22⋊C4—41no—
95C13×C22⋊C4—41no—
96C13×C22⋊C4—41no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4M1614yescomplemented
99C2×#385C2×C1311yescharacteristic
100#1462C2×C1311yescharacteristic
101#1462C2×C1311yescharacteristic
102#1326C2×C1314yescomplemented
103C23×C13—22no—
104C23×C13—22no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—24no—
108C23×C13—24no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—42no—
114C23×C13—48no—
115C23×C13—48no—
116C23×C13—42no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—42no—
122C23×C13—42no—
123C23×C13#9911yescharacteristic
124C23×C13#9911yescharacteristic
125C23×C13#10112yes—
126C23×C13C2×C22⋊C411yescharacteristic
127C23×C13C2×M1612yes—
128C2×C4×C13—24no—
129C2×C4×C13—24no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—42no—
135C2×C4×C13—48no—
136C2×C4×C13—42no—
137C2×C4×C13—42no—
138C2×C4×C13—44no—
139C2×C4×C13—48no—
140C2×C4×C13—44no—
141C2×C4×C13—42no—
142C2×C4×C13—44no—
143C2×C4×C13—42no—
144C2×C4×C13—42no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—44no—
150C2×C4×C13—81no—
151C2×C4×C13—81no—
152C8×C13—82no—
153C8×C13—82no—
154C24×C4C4×C1311yescharacteristic
155C22×C4⋊C4—21no—
156C22×C22⋊C4C4×C1311yescharacteristic
157C22×C22⋊C4C22×C1311yescharacteristic
158#407—21no—
159#407—21no—
160#385—21no—
161#385—21no—
162#385C4×C1312yes—
163#385C22×C1312yes—
164C2×#95—21no—
165#323—21no—
166#323—21no—
167#323C22×C1312yes—
168#323C22×C1312yes—
169C22×C13—24no—
170C22×C13—24no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—22no—
178C22×C13—22no—
179C22×C13—42no—
180C22×C13—42no—
181C22×C13—42no—
182C22×C13—48no—
183C22×C13—48no—
184C22×C13—42no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13AΣL(1,𝔽16)12yes—
190C22×C13#35212yes—
191C22×C13#40711yescharacteristic
192C22×C13C2×#9911yescharacteristic
193C22×C13C2×#10111yescharacteristic
194C4×C13—44no—
195C4×C13—41no—
196C4×C13—44no—
197C4×C13—41no—
198C4×C13—41no—
199C4×C13—41no—
200C25C2×C4×C1311yescharacteristic
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—44no—
205C23×C4—41no—
206C23×C4—41no—
207C23×C4C2×C4×C1312yes—
208C23×C4D4×C1311yescharacteristic
209C23×C4D4×C1311yescharacteristic
210C2×M16—41no—
211C2×M16—41no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—44no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—24no—
217C2×C22⋊C4—41no—
218C2×C22⋊C4—41no—
219C2×C22⋊C4C2×C4×C1312yes—
220C2×C22⋊C4C2×C4×C1311yescharacteristic
221C2×C22⋊C4D4×C1311yescharacteristic
222C2×C22⋊C4D4×C1311yescharacteristic
223C2×C22⋊C4C23×C1311yescharacteristic
224C22⋊C8—22no—
225C22⋊C8—22no—
226C22⋊C8—41no—
227C22⋊C8—41no—
228#95—22no—
229#95—22no—
230C2×C13—21no—
231C2×C13—22no—
232C2×C13—22no—
233C2×C13—21no—
234C2×C13—42no—
235C2×C13—42no—
236C2×C13#146311yescharacteristic
237C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
238C2×C13C2×#35211yescharacteristic
239C24—21no—
240C24—21no—
241C24—22no—
242C24—22no—
243C24—42no—
244C24—42no—
245C24C13×C22⋊C411yescharacteristic
246C24C13×C22⋊C411yescharacteristic
247C24C22×C4×C1311yescharacteristic
248C22×C4—24no—
249C22×C4—24no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—44no—
257C22×C4—44no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—48no—
263C22×C4—44no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—42no—
267C22×C4—44no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4C13×C22⋊C411yescharacteristic
271C22×C4C13×C22⋊C411yescharacteristic
272C22×C4C2×D4×C1311yescharacteristic
273C22×C4C2×D4×C1311yescharacteristic
274M16—82no—
275M16—82no—
276C2×C8—42no—
277C2×C8—42no—
278C4⋊C4—44no—
279C4⋊C4—44no—
280C22⋊C4—24no—
281C22⋊C4—22no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4C13×M1614yescomplemented
287C13#1151711yescharacteristic, direct product factor, Sylow
288C23—21no—
289C23—21no—
290C23—22no—
291C23—22no—
292C23—24no—
293C23—24no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—42no—
303C23—48no—
304C23—48no—
305C23—42no—
306C23—42no—
307C23—42no—
308C23C13×#9911yescharacteristic
309C23C13×#9911yescharacteristic
310C23C13×#10112yes—
311C23C2×C13×C22⋊C411yescharacteristic
312C23C2×C13×M1612yes—
313C2×C4—24no—
314C2×C4—24no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—44no—
322C2×C4—48no—
323C2×C4—42no—
324C2×C4—48no—
325C2×C4—44no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—44no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—44no—
335C2×C4—81no—
336C2×C4—81no—
337C8—82no—
338C8—82no—
339C22—24no—
340C22—24no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—22no—
348C22—22no—
349C22—42no—
350C22—42no—
351C22—42no—
352C22—42no—
353C22—48no—
354C22—48no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22C13×AΣL(1,𝔽16)12yes—
360C22C13×#35212yes—
361C22C13×#40711yescharacteristic
362C22C2×C13×#9911yescharacteristic
363C22C2×C13×#10111yescharacteristic
364C4—44no—
365C4—41no—
366C4—44no—
367C4—41no—
368C4—41no—
369C4—41no—
370C2—21no—
371C2—21no—
372C2—22no—
373C2—22no—
374C2—42no—
375C2—42no—
376C2C13×#146311yescharacteristic
377C2C2×C13×AΣL(1,𝔽16)11yescharacteristic
378C2C2×C13×#35211yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC24C22×C4×C13
Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC25×C13C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C24×C13 ◁ C22×C13×C22⋊C4 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C13×#1326C2semidirect
50. #11517C13direct (N × H)
98. C13×C22⋊C4M16semidirect
102. #1326C2×C13semidirect
286. C22⋊C4C13×M16semidirect
287. C13#11517direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C13×#3852
C13×#14622
C13×#13262
#1151713